A psychology professor assigns letter grades on a test according to the following scheme. A: Top 11% of scores B: Scores below the top 11% a

Question

A psychology professor assigns letter grades on a test according to the following scheme. A: Top 11% of scores B: Scores below the top 11% and above the bottom 61% C: Scores below the top 39% and above the bottom 16% D: Scores below the top 84% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 81.8 and a standard deviation of 7.8. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

in progress 0
Adalyn 2 weeks 2021-09-13T14:07:03+00:00 1 Answer 0

Answers ( )

    0
    2021-09-13T14:08:30+00:00

    Answer: the minimum score required for an A grade is 91

    Step-by-step explanation:

    Since the scores on the test are normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x – µ)/σ

    Where

    x = scores on the test.

    µ = mean score

    σ = standard deviation

    From the information given,

    µ = 81.8

    σ = 7.8

    The probability value for the scores in the top 11% would be (1 – 11/100) = (1 – 0.11) = 0.89

    Looking at the normal distribution table, the z score corresponding to the probability value is 1.23

    Therefore,

    1.23 = (x – 81.8)/7.8

    Cross multiplying by 114, it becomes

    1.23 × 7.8 = x – 81.8

    9.594 = x – 81.8

    x = 9.594 + 81.8

    x = 91 rounded to the nearest whole number.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )